Question

X2-6x-9/x=x2-4x-9/x2-6x-9

Answer 1

Question :

(x2-6x-9)/x)=((x2-4x-9)/(x2-6x-9)

Answer :

x = 5/2 - √ 61/4 ( Ans )

Explanation:

Solving x2-5x-9 = 0 by Completing The Square .

Add 9 to both side of the equ.

x2-5x = 9

now take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4

Add 25/4 to both sides of the equ.:

On the right hand side we have :

9 + 25/4 or, (9/1)+(25/4)

The common denominator of the two fractions is 4 Adding (36/4)+(25/4) gives 61/4

So adding to both sides we got :

x2-5x+(25/4) = 61/4

Adding 25/4 :

x2-5x+(25/4) =

(x-(5/2)) • (x-(5/2)) =

(x-(5/2))2

Things which are equal to the same thing are also equal to one another so

x2-5x+(25/4) = 61/4 and

x2-5x+(25/4) = (x-(5/2))2

according to the law of transitivity,

(x-(5/2))2 = 61/4

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x-(5/2))2 is

(x-(5/2))2/2 =

(x-(5/2))1 =

x-(5/2)

Now, applying the Square Root Principle to Eq. we will get

x-(5/2) = √ 61/4

Add 5/2 to both sides to obtain:

x = 5/2 + √ 61/4

A square root has two values one positive and one negative

x2 - 5x - 9 = 0

so it has two solutions

so, x = 5/2 + √ 61/4

or

x = 5/2 - √ 61/4 ( Ans )

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